each side of an equilateral triangle measures 12 cm find the height of the triangle
In an equilateral triangle, the height bisects the base and forms a right angle. Therefore, we can use the Pythagorean theorem to find the height.
Let h be the height of the triangle.
Using the Pythagorean theorem: h^2 + (12/2)^2 = 12^2
Simplifying: h^2 + 6^2 = 144
h^2 + 36 = 144
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides: h = √108
Simplifying: h ≈ 10.39 cm
Therefore, the height of the equilateral triangle is approximately 10.39 cm.
To find the height of an equilateral triangle, we can use the Pythagorean theorem.
Since an equilateral triangle has all sides equal, we can draw a line from one of the vertices to the center of the opposite side, splitting the triangle into two right triangles.
Let's label the height of the triangle as 'h', and one side of the triangle as 's'.
Now, since the triangle is equilateral, all sides are 12 cm, so s = 12 cm.
The height 'h' divides the equilateral triangle into two congruent right triangles, where the base of each right triangle is half of one side.
Therefore, the base of each right triangle is s/2 = 12/2 = 6 cm.
Using the Pythagorean theorem, we have:
hypotenuse^2 = base^2 + height^2
In this case, the hypotenuse is 12 cm, the base is 6 cm, and we want to find the height 'h'.
So, plugging in the values:
12^2 = 6^2 + h^2
Simplifying:
144 = 36 + h^2
Subtracting 36 from both sides:
144 - 36 = h^2
108 = h^2
Taking the square root of both sides (remembering to consider both positive and negative square roots since height can be positive or negative):
h = ±√108
Simplifying the square root:
h = ±6√3
So, the height of the equilateral triangle measures ±6√3 cm.